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It is proved that the equation x ^ 3-3x = 1 has at least one real root in (1,2)
It is proved that if f (x) = x ^ 3-3x-1, then f '(x) = 3x ^ 2-3
∵x>1, ∴x^2>1, ∴3x^2-3>0
That is to say, f '(x) > 0, the function f (x) increases monotonically on (1,2)
And f (1) = - 10
There is at least one intersection point between F (x) and X axis
That is, the equation x ^ 3-3x = 1 has at least one real root in (1,2)
Hope to adopt! If you have any questions, please ask!
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